The need for compact, low cost, high sensitivity wide bandwidth accelerometers is strongly felt in a number of scientific and technical fields. Among the applications are vehicle health monitoring, guidance and control, acceleration measurement in microgravity experiments, detection of underwater acoustics and seismology. For many of these applications, recent work has been focused on miniaturization to allow new deployment scenarios, and to allow use of low-cost fabrication techniques such as silicon micromachining.
It is important to consider the fundamental principles of accelerometers. A simple accelerometer consists of a spring supported proof mass, with damping, and a position sensor for measuring the displacement of the proof mass relative to the support structure. In this simple accelerometer, only the proof mass is spring-suspended from the support structure; this is called a "single-element structure". The spring-proof mass system is characterized by a natural frequency ##EQU1## where k is the spring constant and m is the proof mass. For frequencies below this natural frequency, the displacement of the proof mass relative to a support, x.sub.r, is given by ##EQU2## where a.sub.s is the acceleration of the support structure. In this frequency range, therefore, the mechanical system acts as an acceleration-to-displacement transducer. The displacement is measured with a position sensor. The output of the position sensor is dependent upon a.sub.s, and thus serves as a measure of the acceleration of the support structure. For a given sensitivity of the position sensor, equation (1) indicates that the acceleration sensitivity of the device can be improved by reducing .omega..sub.o, either by softening the support spring or by increasing the proof mass. Normally accelerometer dynamics are constrained in the following manner. The minimum acceleration to be detected determines the required resolution. The displacement resolution available from the best transducer for the particular application determines the minimum displacement to be detected. Using Equation 2, the upper limit on the resonant frequency of the proof mass is then determined. For example, an acceleration resolution of 10.sup.-8 g/.sqroot.Hz and a displacement resolution of 10.sup.-3 .ANG./.sqroot.Hz require a resonant frequency less than 150 Hz.
For many applications, it is necessary to impose force-feedback control of the transducer to provide linear response over a wide dynamic range. In normal accelerometers, this is accomplished by feedback-controlling the position of the proof mass. However, this is difficult in the case of high sensitivity, wide-bandwidth accelerometers because the feedback system becomes unstable at the resonant frequency of the proof mass. If signals above the resonance of the proof mass are of interest, force feedback cannot be used.
Once the resonant frequency of the mechanical system is chosen, (thereby setting the displacement and bandwidth of the mechanical system) it would appear, from equations (1) and (2), that the proof mass of an accelerometer can be reduced to an arbitrarily small value so long as the spring constant is reduced by a comparable amount. However, as the proof mass is reduced, thermal noise appears in the motion of the mass. This noise can be shown to be completely analogous to Johnson noise in a resistor. It gives rise to a frequency-independent, thermal-noise equivalent, acceleration, TNEA, of the support defined as ##EQU3## where m is the proof mass value, .omega..sub.o is the resonant frequency, k.sub.B is Boltzmann's constant, T is temperature, and Q is the quality factor of the mechanical system. That the TNEA is frequency independent, above as well as below .omega..sub.o, is a consequence of the fact that the thermally-induced motion of the proof mass, and the acceleration response of the mechanical system (x.sub.r /a.sub.s) have identical frequency response. Therefore, their ratio (i.e., TNEA) is frequency independent. TNEA is simply the acceleration corresponding to the thermal motion of the proof mass. In the absence of other noise sources, it sets a lower limit on the acceleration that can be measured with the device.
Traditionally, accelerometer designers have avoided the effects of TNEA by using a large proof mass. However, lower damping (high Q) also could be used to reduce the TNEA for a given proof mass value and resonant frequency. Q can be increased by evacuating a can housing the accelerometer, thus reducing the viscous damping from the air.
Miniaturization of sensors has been enabled by the development of silicon micromachining technology, and miniature accelerometers have been described by a number of authors. However, to meet needs for low-cost high-performance, miniature accelerometers and displacement sensors, conventional transducer technologies relying on capacitive, optical, inductive, or piezo transducers often impose incompatible mass, volume, or power requirements. Thus, miniaturization requires new approaches. To achieve substantial reductions in size relative to conventional accelerometers, new position sensing techniques which are sensitive to extremely small displacements are required. Electron tunneling is such a technique.
Displacement transducers based on electron tunneling through a narrow vacuum or air barrier have been shown to offer high sensitivity which results from the exponential dependence of tunnel current on tunnel electrode spacing. For example, employing a tip similar to those used in Scanning Tunneling Microscopy (STM), an acceleration resolution of 10.sup.-5 g/.sqroot.Hz with a bandwidth of 3 kHz has been observed. A tunneling transducer similar to those of the accelerometers described below, coupled with a miniature Golay cell fabricated by silicon micromachining, has also been constructed as a high-sensitivity infrared detector.
In operation of a tunnel tip in an STM mode, a tunnel current I is established between a tip and a counterelectrode by a small voltage bias V. In typical STM operation, feedback circuitry controls the vertical position of the tip by means of a piezoelectric transducer so as to maintain the tunnel current constant, thereby also maintaining the electrode spacing s constant, while the specimen is scanned laterally. Tunnel current I depends on electrode spacing s as ##EQU4## where .phi.=1.025.ANG..sup.-5 eV.sup.-1/2, .phi. is the height of the tunnel barrier, and the bias voltage V is small compared to .phi.. For typical values of .phi. and s (0.5 eV and 10.ANG., respectively), the current varies by a factor of two for each .ANG. change in electrode separation. Because of this extreme sensitivity to position, the tip-to-substrate separation is maintained constant to high precision for lateral scanning over topography. The output of the feedback circuitry is also used as a measure of the tip's vertical position. The tunnel transducer's sensitivity to position is superior to that of other compact transducers and is orders of magnitude better than compact capacitive sensors, for example. Also, the sensitivity of a tunnel transducer is independent of device size because of the extremely small size of the tunneling tip. Thus, miniaturization of the transducer causes no reduction in sensitivity. Micromachining of silicon through the use of anisotropic etchants and doping to control etching allows fabrication of sensors completely from single crystal silicon, coupled with thin film deposition. Such micromachined silicon sensors take advantage of precision photolithography and batch processing to facilitate miniaturization and reduce fabrication costs.
A prototype single-element tunneling accelerometer has been fabricated from silicon utilizing a micromachined silicon tip coated with a gold electrode. One electrode of the electron tunneling circuit is mounted on a cantilever supported by a folded cantilever spring. The tunnel electrode gap is adjusted by electrostatic deflection of this cantilever. A feedback circuit maintains the desired tunnel current by controlling this electrostatic deflection. The variations in deflection voltage required to maintain constant tunnel current may be analysed to calculate the applied acceleration. Use of electrostatic deflection in a tunnel sensor is a marked improvement over piezoelectric actuators, as commonly used for tunneling microscopy. In contrast to piezoelectric devices, electrostatic actuators show virtually no hysteresis and drift, and are insensitive to temperature. The response of the electrostatic actuator is a function only of the geometry and mechanical properties of the device, whereas the response of piezoelectric actuators is also dependent on other material characteristics which may not be reproducible between devices and over time. Also, the electrostatic actuator may be readily incorporated into a microelectronic package in a batch fabricated process.
The silicon tip is formed directly on the silicon substrate, or alternatively, on the silicon proof mass, by undercutting a 60.times.60 micron square of SiO.sub.2 with ethylenediamine pyrocatechol (EDP) etchant until the fragment of oxide is carried away, leaving a pyramidal tip. The cantilever area for this prototype is approximately 1 cm.sup.2 with a mass of 30 mg. The measured spring constant is 60 N/m, giving a calculated natural frequency of 225 Hz.
The resolution of the device is determined by both the responsivity and the dominant noise sources. Since the measured noise includes contributions from the laboratory, the fundamental noise of the sensor may be less. The measured current noise at 10 Hz and 1 kHz is approximately 2.3.times.10.sup.-12 and 2.5.times.10.sup.-13 A/.sqroot.Hz, respectively, for an operating current of 1.3 nA and bias of 100 mV. This noise was measured with a feedback loop bandwidth less than 0.1 Hz, in order to prevent the feedback loop from autocorrecting for the noise in the tunnel current above that frequency. Utilizing determinations of the tunnel transducer displacement responsivity of 0.94 nA/.ANG., the displacement resolution of the tunnel transducer is 2.4.times.10.sup.-3 and 2.7.times.10.sup.-4 .ANG./.sqroot.Hz at 10 Hz and 1 kHz, respectively. The corresponding acceleration resolutions of the sensor system are 5.times.10.sup.-8 and 1.2.times.10.sup.-7 g/.sqroot.Hz (below the natural frequency of the suspended mass, the system resolution is different than the tunnel transducer resolution; they are related through the second part of Equation 6 below). The actual resolution of the sensor may be greater, since the measured noise includes contributions from the laboratory. This sensitivity is several orders of magnitude better than conventional compact accelerometers. For the above prototype, the proof mass position relative to the counterelectrode is controlled and held constant by the feedback control system. The transducer signal is derived from the electrostatic force required to maintain its position relative to the counterelectrode. Stable operation of the feedback circuitry is restricted to frequencies below the natural frequency of the suspended proof mass, about 225 Hz for this device. However, many applications require a larger bandwidth.
Prior art in the form of issued U.S. Patents relevant to the present invention in varying degrees, includes the following:
U.S. Pat. No. 4,675,670 to Lalonde et al is directed to an apparatus for the dynamic and non-contact measurement of small distances using two conductive plates that are parallel, superimposed and electrically insulated from one another and using circuitry to measure a current between these plates and a conductive surface that is an inverse function of the distance to be measured. The circuitry includes a generator supplying up to 100 MHz and up to 100 Volts. The apparatus shown for measuring the air gap in a rotary machine has sensor 7 comprising plates 9 and 11 separated by insulation 13 mounted on and insulated from surface 3. The signal generator supplies the fixed capacitor between the plates and the variable capacitor between plate 11 and surface 5 with a high frequency signal. Circuitry 19 detects the resultant current which is inversely proportional to the distance and circuitry 21 processes the signal by biasing and linearizing the current signal to provide a distance signal.
U.S. Pat. No. 5,008,774 to Bullis et al is directed to a capacitive accelerometer with mid-plane proof mass adapted to register acceleration coaxial with axis 230. The apparatus has a three plate capacitor with rigid top and bottom plates 20, 30 and hinged proof mass 110 comprised of two silicon slabs 112, 114 with a conductive interface region 115. This micromachined unit is connected to the electronic portion 310 made of straightforward circuits to sense capacitance by monitoring the unbalance of the high frequency bridge circuit of which the three plate capacitor forms a part.
U.S. Pat. No. 3,723,866 to Michaud et al is directed to a movement measuring sensor comprising a rule having parallel surfaces and a slider having parallel surfaces opposite to the first parallel surfaces and movable relatively to the rule in a direction parallel to the surfaces. The surfaces have conductive strips to form two capacitors in a series relationship. This rule 10 for measuring to an accuracy of 0.1 micron is read by determining the value of capacitance between the rule and the slider and it is preferable to use the indirect method to determine the value of the capacitor, indirect methods being more accurate than direct methods. The voltage method using a high frequency generator operating in the megahertz range to energize the circuit is preferable to the non-linear oscillator method.
U.S. Pat. No. 4,823,230 to Tiemann is directed to a pressure-to-capacitance transducer of the deflecting membrane type having increased dynamic range. The transducer 10 fabricated of a non-conductive material such as ceramic or a semiconductor substrate 10-1 has a first conductive electrode 11 formed on the surface of the substrate. A first insulator material 12 is fabricated over the electrode 11 and an insulating wall 14 fabricated upon the substrate 10-1 enclosing the entire transducer area. A second electrode 18 of thin film elastically-deflecting conductive material is fabricated in attachment to the wall top portion so as to complete a pressure-tight cavity 10c. This cavity is filled with a reference volume of a reference gas at a reference pressure to give the physical characteristics desired to the transducer. The capacitance between the first electrode 11 and second electrode 18 can be measured by electronic circuitry--it will be understood that this circuitry can be integrated into the substrate 10-1.
U.S. Pat. No. 4,364,008 to Jacques is directed to a moisture measuring device 10 comprising a microwave generator 12 operating between 100 MHz and 20 GHz, a resonant cavity guiding means 14, typically a coaxial cable and a probe 16 in several embodiments, some with switching provided manually or by computer 22. The Shottky diode detector 18 provides the moisture signal through the dc circuit 20 to the computer 22.
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